Question

As a computer technician, andre makes $20 per hour to diagnose a problem and $25 per hour to fix a problem. he works fewer than 10 hours per week, but wants to make at least $200 per week. the inequalities 20x 25y ≥ 200 and x y

Answer 1

The subject of this question is Mathematics because it involves solving inequalities and working with variables.

Step-by-step explanation:

The subject of this question is Mathematics because it involves solving inequalities and working with variables.

In this case, the student wants to make at least $200 per week and is paid $20 per hour to diagnose a problem and $25 per hour to fix a problem. We can represent the number of hours spent diagnosing as 'x' and the number of hours spent fixing as 'y'.

The inequality 20x + 25y ≥ 200 represents the student's goal of making at least $200 per week. The second inequality, x + y < 10, indicates that the student works fewer than 10 hours per week.

Answer 2

The true statements regarding the graph are:

- The line representing
`\( 20x + 25y \geq 200 \)` is solid, and the graph is shaded above the line.

- The overlapping region contains the point (4, 5).

The other statements are false based on the incorrect descriptions of the slopes and shading directions.

To determine the properties of the graph of the solution set for the given inequalities, let's analyze each statement:

1. The line
`\( 20x + 25y \geq 200 \)` has a positive slope and a negative y-intercept.

- The slope of a line in the form
`\( Ax + By = C \)` is
`\( -A/B \)`. For this line, the slope is
`\( -20/25 \)` which simplifies to
`\( -4/5 \)`, so it is negative.

- The y-intercept occurs when
`\( x = 0 \)`. Setting
`\( x = 0 \)` in the inequality gives
`\( 25y \geq 200 \)`, which results in
`\( y \geq 8 \)`. This is a positive y-intercept.

- Therefore, this statement is false.

2. The line
`\( x + y < 10 \)` has a negative slope and a positive y-intercept.

- The standard form of this line is
`\( -x + y = 10 \)` with a slope of
`\( -(-1/1) = 1 \)`, which is positive.

- The y-intercept is the value of
`\( y \)` when
`\( x = 0 \)`, which is
`\( y = 10 \)`, a positive y-intercept.

- This statement is also false since the slope is not negative.

3. The line representing
`\( 20x + 25y \geq 200 \)` is solid and the graph is shaded above the line.

- The inequality \( \geq \) indicates a solid line because it includes the points on the line.

- The inequality is greater than, which means the graph will be shaded above the line.

- This statement is true.

4. The line representing
`\( x + y < 10 \)` is dashed and the graph is shaded above the line.

- The inequality \( < \) indicates a dashed line because it does not include the points on the line.

- However, since it is less than, the graph will be shaded below the line, not above.

- This statement is partially true regarding the dashed line but false regarding the shading.

5. The overlapping region contains the point (4, 5).

- To check if a point is in the solution set of an inequality, we can substitute the values into both inequalities.

- For
`\( 20x + 25y \geq 200 \): \( 20(4) + 25(5) = 80 + 125 = 205 \)`, which is greater than 200.

- For
`\( x + y < 10 \)`:
`\( 4 + 5 = 9 \)`, which is less than 10.

- So, the point (4, 5) satisfies both inequalities and is in the overlapping region.

- This statement is true.

From the analysis, the true statements regarding the graph are:

- The line representing
`\( 20x + 25y \geq 200 \)` is solid, and the graph is shaded above the line.

- The overlapping region contains the point (4, 5).

The other statements are false based on the incorrect descriptions of the slopes and shading directions.

the complete Question is given below:

week, but wants to make at least $200 per week. The inequalities 20x + 25y ≥ 200 and x + y < 10 represent the situation. Which is true of the graph of the solution set? Check all that apply. The line 20x + 25y ≥ 200 has

As a computer technician, Andre makes $20 per hour to diagnose a problem and $25 per hour to fix a problem. He works fewer than 10 hours per week, but wants to make at least $200 per week. The inequalities 20x + 25y ≥ 200 and x + y < 10 represent the situation. Which is true of the graph of the solution set? Check all that apply. The line 20x + 25y ≥ 200 has a positive slope and a negative y-intercept. The line x + y < 10 has a negative slope and a positive y-intercept. The line representing 20x + 25y ≥ 200 is solid and the graph is shaded above the line. The line representing x + y < 10 is dashed and the graph is shaded above the line. The overlapping region contains the point (4, 5).